Conventional carbon fibers for use in carbon-fiber composite materials, when a polyacrylonitrile-based precursor is used as starting fibers, are commonly produced by subjecting first the precursor to flame-resisting treatment in an oxidizing atmosphere at temperatures of 200.degree. to 300.degree. C., then carbonizing the treated fibers in an inert atmosphere, and generally subjecting the carbonized fibers to gas-phase or liquid-phase oxidation to enhance the adhesion of the carbon fibers to the matrix, followed by treating the fibers with a suitable sizing agent for the purpose of inhibiting the fiber breaking and fuzzing which may take place during handling of the fiber. However, the composite materials containing these carbon fibers are still insufficient in the adhesion of the fibers to the matrix. In particular, the compressive strength after impact (CAI) is generally on a level of 193.2.times.10.sup.3 KPa (19.7 kg/mm.sup.2) when the impact force is 68.1 kg/cm (1500 lb in/in), as shown in Eur. Patent Application Laid-Open No. 132853, Table IV, Example 35. Thus, it is the present situation that the CAI is extremely difficult to improve by using a matrix having such a high heat resistance as shown in Example 35 mentioned above.
While an average CAI of 45.3 ksi (31.8 kg/mm.sup.2) is obtained in Eur. Patent Application Laid-Open No. 133280, Examples 6, 7, and 8, which aimed at improving the CAI, this type of composite has a tough layer called an interlief between prepreg layers and this inserted layer hinders the raise of the fiber content by volume, gives two different faces to the prepreg, and makes the handleness inferior.
On the other hand, it is required in the aircraft industry to improve the CAI to 27 kg/mm.sup.2 or more in order to reduce the weight of plane bodies and it is desired to develop a composite material containing no special layer for the purpose of satisfying this requirement.